The Effects of Logo on Children's Conceptualizations of Angle and Polygons

It has been claimed that in Logo programming children learn mathematics by using concepts that aid them in understanding and directing the turtle's movements. The fundamental basis for this claim is that appropriate Logo environments can help children elaborate on, and become cognizant of, the mathematics implicit in certain kinds of intuitive thinking. To investigate this claim, 12 fourth graders were interviewed three times, at the beginning, middle, and end of 40 sessions of Logo graphics programming experience. The six Logo children, but not the comparison children, progressed from their original intuitive notions to more mathematically sophisticated and elaborate ideas of angle, angle size, and rotation. In addition, more Logo children explicitly mentioned geometric properties of shapes, indicating that they were beginning to think of the shapes in terms of their properties instead of as visual gestalts. Thus, there was support for the hypothesis that Logo experiences, especially those enriched with appropriate activities and discussions, can help children become cognizant of their mathematical intuitions and move to higher levels of geometric thinking.